University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-06548520111029Cover Special Issue vol. 8, no. 5, October 2011-0EN10.22111/ijfs.2011.2866http://ijfs.usb.ac.ir/article_2866.htmlhttp://ijfs.usb.ac.ir/article_2866_7c95e1e920951e2eb9a6e5bcecdb68b0.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-06548520111006FUZZY ORDERED SETS AND DUALITY FOR FINITE FUZZY
DISTRIBUTIVE LATTICES112ENAbdelazizAmrouneDepartment of Mathematics, M’Sila University, P.O. Box 166,
M’Sila 28000, Algeriaaamrounedz@yahoo.frBijanDavvazDepartment of Mathematics, Yazd University, Yazd, Irandavvaz@yazduni.ac.ir10.22111/ijfs.2011.294The starting point of this paper is given by Priestley’s papers,
where a theory of representation of distributive lattices is presented. The purpose
of this paper is to develop a representation theory of fuzzy distributive
lattices in the finite case. In this way, some results of Priestley’s papers are
extended. In the main theorem, we show that the category of finite fuzzy
Priestley spaces is equivalent to the dual of the category of finite fuzzy distributive
lattices. Several examples are also presented.Fuzzy ordered relation,Fuzzy ordered set,Fuzzy lattice,Fuzzy Priestley
space,Homomorphism of fuzzy lattices,Homomorphism of fuzzy Priestley spaceshttp://ijfs.usb.ac.ir/article_294.htmlhttp://ijfs.usb.ac.ir/article_294_0585ff76677fb9b648afed68597a373f.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-06548520111006ON ALGEBRAIC AND COALGEBRAIC CATEGORIES OF
VARIETY-BASED TOPOLOGICAL SYSTEMS1330ENSergey A.SolovyovDepartment of Mathematics, University of Latvia, Zellu iela 8,
LV-1002 Riga, Latvia and Institute of Mathematics and Computer Science, University
of Latvia, Raina bulvaris 29, LV-1459 Riga, Latviasolovjovs@fme.vutbr.cz10.22111/ijfs.2011.295Motivated by the recent study on categorical properties of latticevalued
topology, the paper considers a generalization of the notion of topological
system introduced by S. Vickers, providing an algebraic and a coalgebraic
category of the new structures. As a result, the nature of the category
TopSys
of S. Vickers gets clari ed, and a metatheorem is stated, claiming that (latticevalued)
topology can be embedded into algebra.Algebra,(Co)algebraic category,(Co)re
ective subcategory,Latticevalued
topology,Powerset operator,S-quantale,Topological category,Topological system,Varietyhttp://ijfs.usb.ac.ir/article_295.htmlhttp://ijfs.usb.ac.ir/article_295_78807b744112194d3dde64cbaf1cf650.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-06548520111006ALGEBRAIC GENERATIONS OF SOME FUZZY POWERSET
OPERATORS3158ENQi-YeZhangSchool of Mathematics and Systems Science, Beihang University, Beijing
100191, China and LMIB of the Ministry of Education, Beijing 100191, Chinazhangqiye@buaa.edu.cn10.22111/ijfs.2011.296In this paper, let $L$ be a completeresiduated lattice, and let {bf Set} denote the category of setsand mappings, $LF$-{bf Pos} denote the category of $LF$-posets and$LF$-monotone mappings, and $LF$-{bf CSLat}$(sqcup)$, $LF$-{bfCSLat}$(sqcap)$ denote the category of $LF$-completelattices and $LF$-join-preserving mappings and the category of$LF$-complete lattices and $LF$-meet-preserving mappings, respectively. It isproved that there are adjunctions between {bf Set} and $LF$-{bf CSLat}$(sqcup)$, between $LF$-{bfPos} and $LF$-{bf CSLat}$(sqcup)$, and between $LF$-{bf Pos} and$LF$-{bf CSLat}$(sqcap)$, that is, {bf Set}$dashv LF$-{bf CSLat}$(sqcup)$, $LF$-{bfPos}$dashv LF$-{bf CSLat}$(sqcup)$, and $LF$-{bf Pos}$dashv$$LF$-{bf CSLat}$(sqcap)$. And a usual mapping $f$ generates thetraditional Zadeh forward powerset operator $f_L^rightarrow$ andthe fuzzy forward powerset operators $widetilde{f}^rightarrow,widetilde{f}_ast^rightarrow, widetilde{f}^{astrightarrow}$defined by the author et al via these adjunctions. Moreover, it is also shownthat all the fuzzy powerset operators mentioned above can be generated by the underlying algebraic theories.Complete residuated lattice,$L$-fuzzy poset,Category,Adjunction,Algebraic theory,Powerset theory,Algebraic generationhttp://ijfs.usb.ac.ir/article_296.htmlhttp://ijfs.usb.ac.ir/article_296_80d019c2a46e66b3c7ab1031e2569b3e.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-06548520111006NEW DIRECTION IN FUZZY TREE AUTOMATA5968ENS.MoghariDepartment of Mathematics, Science Faculty, Alzahra University,
Vanak, Tehran, Irans moghari@student.alzahra.ac.irM. M.ZahediDepartment of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iranzahedi mm@mail.uk.ac.irR.AmeriCollege of Sciences, Tehran University, P.O. Box 14155-6455, Tehran, Iranameri@umz.ac.ir10.22111/ijfs.2011.297In this paper, our focus of attention is the proper propagationof fuzzy degrees in determinization of $Nondeterministic$ $Fuzzy$$Finite$ $Tree$ $Automata$ (NFFTA). Initially, two determinizationmethods are introduced which have some limitations (one inbehavior preserving and other in type of fuzzy operations). Inorder to eliminate these limitations and increasing theefficiency of FFTA, we define the notion of fuzzy complex stateand $Complex$ $FFTA$ (CFFTA). Also, we define$nabla$-normalization operation in algebra of fuzzy complexstate to solve the multi membership state problem in fuzzyautomata. Furthermore, we discuss the relationship between FFTAand CFFTA. Finally, determinization of CFFTA is presented.Fuzzy tree automata,Complex fuzzy tree automata,Determinizationhttp://ijfs.usb.ac.ir/article_297.htmlhttp://ijfs.usb.ac.ir/article_297_0c27ea3b6611895f9ba1d96628fb269a.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-06548520111006THE CONNECTION BETWEEN SOME EQUIVALENCE
RELATIONS ON FUZZY SUBGROUPS6980ENAliIranmaneshDepartment of Mathematics, Tarbiat Modares University, P.O.
Box: 14115-137, Tehran, Iraniranmana@modares.ac.irHosseinNaraghiTarbiat Modares University, P.O. Box: 14115-137, Tehran, Iranh.naraghi56@gmail.com10.22111/ijfs.2011.298This paper, deals with some equivalence relations in fuzzy subgroups.
Further the probability of commuting two fuzzy subgroups of some
finite abelian groups is defined.Dihedral group,Equivalence relation,Fuzzy subgroups,Finite cyclic
group,p − group,Probabilityhttp://ijfs.usb.ac.ir/article_298.htmlhttp://ijfs.usb.ac.ir/article_298_9700a0526c25c8f4d3ca42e4af01ae3f.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-06548520111006﻿A NEW WAY TO FUZZY h-IDEALS OF HEMIRINGS81101ENYunqiangYinSchool of Sciences, East China Institute of Technology, Fuzhou,
Jiangxi 344000, Chinayunqiangyin@gmail.comJianmingZhanDepartment of Mathematics, Hubei Institute for Nationalities, Enshi,
Hubei Province 445000, Chinazhanjianming@hotmail.comXiaokunHuangDepartment of Mathematics, Honghe University, Mengzi, Yunnan
661100, Chinaboyhxk@163.com10.22111/ijfs.2011.299By means of a kind of new idea, we consider the $(in,ivq)$-fuzzy$h$-ideals of a hemiring. First, the concepts of $(in,ivq)$-fuzzyleft(right) $h$-ideals of a hemiring are provided and some relatedproperties are investigated. Then, a kind of quotient hemiring ofa hemiring by an $(in,ivq)$-fuzzy $h$-ideal is presented andstudied. Moreover, the notions of generalized $varphi$-compatible$(in,ivq)$-fuzzy left(right) $h$-ideals of a hemiring areintroduced and some properties of them are provided. Finally, therelationships among $(in,ivq)$-fuzzy $h$-ideals, quotienthemirings and homomorphisms are explored and several homomorphismtheorems are provided.Hemiring,$(\in,\ivq)$-fuzzy
left(right) $h$-ideals,Generalized $\varphi$-compatible
$(\in,\ivq)$-fuzzy left(right) $h$-idealshttp://ijfs.usb.ac.ir/article_299.htmlhttp://ijfs.usb.ac.ir/article_299_aaa3f3b3c23fef1a9e66044b328b54d2.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-06548520111006FUZZY REFLEXIVITY OF FELBIN'S TYPE FUZZY NORMED
LINEAR SPACES AND FIXED POINT THEOREMS
IN SUCH SPACES103115ENT.BagDepartment of Mathematics, Visva-Bharati, Santiniketan-731235, West Ben-
gal, Indiatarapadavb@gmail.comS. K.SamantaDepartment of Mathematics, Visva-Bharati, Santiniketan-731235, West
Bengal, Indiasyamal 123@yahoo.co.in10.22111/ijfs.2011.300An idea of fuzzy reexivity of Felbin's type fuzzy normed linear
spaces is introduced and its properties are studied. Concept of fuzzy uniform
normal structure is given and using the geometric properties of this concept
xed point theorems are proved in fuzzy normed linear spaces.Fuzzy normed linear space,Fuzzy re
exive space,Fuzzy uniform
normal structure,Fixed point theoremhttp://ijfs.usb.ac.ir/article_300.htmlhttp://ijfs.usb.ac.ir/article_300_624227350b1d0dcbab964c4fb90430d5.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-06548520111006ON FELBIN’S-TYPE FUZZY NORMED LINEAR SPACES AND
FUZZY BOUNDED OPERATORS117130ENMohammadJanfadaDepartment of Mathematics, Sabzevar Tarbiat Moallem University,
Sabzevar, Iranmjanfada@gmail.comHamidBaghaniDepartment of Mathematics, Semnan University, Semnan, Iranbaghani@gmail.comOmidBaghaniDepartment of Mathematics, Ferdowsi University of Mashhad, Mashhad,
Iranomid.baghani@gmail.com10.22111/ijfs.2011.301In this note, we aim to present some properties of the space of all
weakly fuzzy bounded linear operators, with the Bag and Samanta’s operator
norm on Felbin’s-type fuzzy normed spaces. In particular, the completeness
of this space is studied. By some counterexamples, it is shown that the inverse
mapping theorem and the Banach-Steinhaus’s theorem, are not valid for
this fuzzy setting. Also finite dimensional normed fuzzy spaces are considered
briefly. Next, a Hahn-Banach theorem for weakly fuzzy bounded linear
functional with some of its applications are established.Fuzzy analysis,Fuzzy number,Fuzzy relationshttp://ijfs.usb.ac.ir/article_301.htmlhttp://ijfs.usb.ac.ir/article_301_74ebb1ab54f2a83281a4bc5d5a3a8241.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-06548520111006GRADUAL NORMED LINEAR SPACE131139ENI.SadeqiDepartment of Mathematics, Sahand university of technology, Tabriz-
Iranesadeqi@sut.ac.irF. Y.AzariDepartment of Mathematics, Sahand university of technology, Tabriz-
Iranfyaqubazari@gmail.com10.22111/ijfs.2011.302In this paper, the gradual real numbers are considered and the
notion of the gradual normed linear space is given. Also some topological
properties of such spaces are studied, and it is shown that the gradual normed
linear space is a locally convex space, in classical sense. So the results in locally
convex spaces can be translated in gradual normed linear spaces. Finally, we
give an example of a gradual normed linear space which is not normable in
classical analysis.Fuzzy interval,Gradual real number,Locally convex spacehttp://ijfs.usb.ac.ir/article_302.htmlhttp://ijfs.usb.ac.ir/article_302_6ea1e8a077e90219b672804fb0f85ca4.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-06548520111006$psi -$weak Contractions in Fuzzy Metric Spaces141148ENMujahidAbbasDepartment of Mathematics, Lahore University of Management Sci-
ences, 54792- Lahore, Pakistanmujahid@lums.edu.pkM.ImdadDepartment of Mathematics, Aligarh Muslim University, 202002, Aligarh,
Indiamhimdad@yahoo.comD.GopalDepartment of Mathematics and Humanities, S. V. National Institute of
Technology, Surat, 395007, Gujarat, Indiagopal.dhananjay@rediffmail.com10.22111/ijfs.2011.303In this paper, the notion of $psi -$weak contraction cite{Rhoades} isextended to fuzzy metric spaces. The existence of common fixed points fortwo mappings is established where one mapping is $psi -$weak contractionwith respect to another mapping on a fuzzy metric space. Our resultgeneralizes a result of Gregori and Sapena cite{Gregori}.Weekly compatible mappings,Fuzzy metric spaces,Common fixed
point,$\psi-$weak contractionshttp://ijfs.usb.ac.ir/article_303.htmlhttp://ijfs.usb.ac.ir/article_303_a705fe8411d5fcf87c600a6746d0841a.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-06548520111006DIMENSION OF FUZZY HYPERVECTOR SPACES149166ENRezaAmeriSchool of Mathematics, Statistics and Computer Science, College of
Sciences, University of Tehran, P. O. Box 14155-6455, Teheran, Iranrameri@ut.ac.irOmid RezaDehghanDepartment of Mathematics, Faculty of Basic Sciences, University
of Bojnourd, Bojnourd, Irandehghan@umz.ac.ir10.22111/ijfs.2011.304In this paper we investigate the algebraic properties of dimension
of fuzzy hypervector spaces. Also, we prove that two isomorphic fuzzy
hypervector spaces have the same dimension.Fuzzy hypervector space,Fuzzy linear independence,Fuzzy basis,Dimensionhttp://ijfs.usb.ac.ir/article_304.htmlhttp://ijfs.usb.ac.ir/article_304_14bfdec4c43880bdbfe530d2df936bd0.pdfUniversity of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-06548520111029Persian-translation Special Issue vol. 8, no. 5, October 2011169179EN10.22111/ijfs.2011.2867http://ijfs.usb.ac.ir/article_2867.htmlhttp://ijfs.usb.ac.ir/article_2867_f04ea4312ef08393949d183a3d63641f.pdf